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A spherical sector is a solid of revolution enclosed by two radii from the center of a sphere. The spherical sector may either be "open" and have a conical hole (left figure; ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

A plane-filling arrangement of plane figures or its generalization to higher dimensions. Formally, a tiling is a collection of disjoint open sets, the closures of which cover ...

Let Omega be a bounded open set in R^d whose boundary partialOmega is at least C^1 smooth and let T:C_c^1(Omega^_)->L^p(partialOmega) (1) be a linear operator defined by ...

A uniquely pancyclic graph is a graph that has exactly one cycle of each length between 3 and the graph's vertex count. Uniquely pancyclic graphs are therefore a special case ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* separates points (i.e., is T2). The weak topology tau_w on X is defined to be the coarsest/weakest ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

A way to display n variables on a two-dimensional surface. For instance, let x be eyebrow slant, y be eye size, z be nose length, etc. The above figures show faces produced ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...